Prefix palindromic length of the Sierpinski word
英文摘要：
The prefix palindromic length $p_{\mathbf{u}}(n)$ of an infinite word $\mathbf{u}$ is the minimal number of concatenated palindromes needed to express the prefix of length $n$ of $\mathbf{u}$. This function is surprisingly difficult to study; in particular, the conjecture that $p_{\mathbf{u}}(n)$ can be bounded only if $\mathbf{u}$ is ultimately periodic is open since 2013. A more recent conjecture concerns the prefix palindromic length of the period doubling word: it seems that it is not $2$-regular, and if it is true, this would give a rare if not unique example of a non-regular function of a $2$-automatic word. For some other $k$-automatic words, however, the prefix palindromic length is known to be $k$-regular. Here we add to the list of those words the Sierpinski word $\mathbf{s}$ and give a complete description of $p_{\mathbf{s}}(n)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
